Yes, it is thought that Elizabeth was given her mother's initialled jewels which included the famous B necklace and also an A necklace which Elizabeth is thought to be wearing in The Whitehall Family Portrait. It is not known what happened to these necklaces after Elizabeth's death.
Could possibly the neclace and gold letters A and B have been burried with Queen Elizabeth 1 at Westminster Abbey? We know that the Tudor Queen Elizabeth wore a ring inside of which was a miniture portrait of her mother Anne. She wore this ring all of her life.